Two particles of equal masses have velocities v⃗1=2 î m / s and v⃗2=2 ĵ m / s. The first parti

step 1 In this question it is given that two particles of equal masses have velocities that is 2 i -cap

Two particles of equal masses have velocities v⃗1=2 î m / s...

Two particles of equal masses have velocities $\vec{v}_{1}=2 \hat{i} \mathrm{~m} / \mathrm{s}$ and $\vec{v}_{2}=2 \hat{j} \mathrm{~m} / \mathrm{s}$. The first particle has an acceleration $\vec{a}_{1}=(3 \hat{i}+3 \hat{j}) \mathrm{m} / \mathrm{s}^{2}$, while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a (a) circle (b) parabola (c) straight line (d) ellipse

Two particles of equal masses have velocities $\vec{v}_{1}=2 \hat{i} \mathrm{~m} / \mathrm{s}$ and $\vec{v}_{2}=2 \hat{j} \mathrm{~m} / \mathrm{s}$. The first particle has an acceleration $\vec{a}_{1}=(3 \hat{i}+3 \hat{j}) \mathrm{m} / \mathrm{s}^{2}$, while the acceleration of the other
particle is zero. The centre of mass of the two particles moves in a
(a) circle
(b) parabola
(c) straight line
(d) ellipse

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Key Concepts

Kinematics of Uniform Acceleration

Kinematics of uniform acceleration deals with motion where the acceleration remains constant over time. In such problems, the position and velocity of an object can be determined using standard equations that relate displacement, initial velocity, acceleration, and time. This concept is crucial in understanding how the center of mass moves when subject to constant external forces.

Vector Addition

Vector addition involves combining multiple vectors to obtain a resultant vector. In the context of motion, this means adding the individual components of velocity and acceleration vectors to determine the net or average effect. Understanding vector addition is essential when analyzing multi-dimensional motion and determining the trajectory of the center of mass.

Center of Mass

The center of mass is the weighted average position of all the mass in a system. For equal masses, it is simply the arithmetic mean of their positions. Analyzing the motion of the center of mass helps simplify the problem by reducing the system's behavior to that of a single point, whose motion is dictated by the average of the individual accelerations and velocities.

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